document.write( "Question 1048008: Need help - Solve cos(x/4) = 1/2 in interval (-6pi,4pi). \n" ); document.write( "
Algebra.Com's Answer #663787 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"cos%28x%2F4%29\"\"%22%22=%22%22\"\"1%2F2\"\r\n" );
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document.write( "\"x%2F4\"\"%22%22=%22%22\"\"matrix%281%2C3%2Cpi%2F3%2B2pi%2Ak%2C%22%3B%22%2C5pi%2F3%2B2pi%2Ak%29\"\r\n" );
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document.write( "We'll take each one individually.\r\n" );
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document.write( "\"x%2F4\"\"%22%22=%22%22\"\"pi%2F3%2B2pi%2Ak\"\r\n" );
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document.write( "Multiply through by 4\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"4pi%2F3%2B8pi%2Ak\"\r\n" );
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document.write( "in interval (-6pi,4pi)}}}\r\n" );
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document.write( "\"-6pi\"\"%22%22%3C%22%22\"\"4pi%2F3%2B8pi%2Ak\"\"%22%22%3C%22%22\"\"4pi\"\r\n" );
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document.write( "Multiply all three sides by 3\r\n" );
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document.write( "\"-18pi\"\"%22%22%3C%22%22\"\"4pi%2B24pi%2Ak\"\"%22%22%3C%22%22\"\"12pi\"\r\n" );
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document.write( "Subtract \"4pi\" from all three sides:\r\n" );
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document.write( "\"-14pi\"\"%22%22%3C%22%22\"\"24pi%2Ak\"\"%22%22%3C%22%22\"\"8pi\"\r\n" );
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document.write( "Divide all three sides by \"24pi\"\r\n" );
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document.write( "\"%28-14pi%29%2F%2824pi%29\"\"%22%22%3C%22%22\"\"%2824pi%2Ak%29%2F%2824pi%29\"\"%22%22%3C%22%22\"\"8pi%2F%2824pi%29\"\r\n" );
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document.write( "\"%28-7%29%2F%2812%29\"\"%22%22%3C%22%22\"\"k\"\"%22%22%3C%22%22\"\"1%2F3\"\r\n" );
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document.write( "The only integer between those values is k = 0.\r\n" );
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document.write( "So one solution is \r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"4pi%2F3%2B8pi%2A0\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"4pi%2F3\"\r\n" );
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document.write( "------------\r\n" );
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document.write( "For the other one,\r\n" );
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document.write( "\"x%2F4\"\"%22%22=%22%22\"\"5pi%2F3%2B2pi%2Ak\"\r\n" );
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document.write( "Multiply through by 4\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"20pi%2F3%2B8pi%2Ak\"\r\n" );
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document.write( "in interval (-6pi,4pi)}}}\r\n" );
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document.write( "\"-6pi\"\"%22%22%3C%22%22\"\"20pi%2F3%2B8pi%2Ak\"\"%22%22%3C%22%22\"\"4pi\"\r\n" );
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document.write( "Multiply all three sides by 3\r\n" );
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document.write( "\"-18pi\"\"%22%22%3C%22%22\"\"20pi%2B24pi%2Ak\"\"%22%22%3C%22%22\"\"12pi\"\r\n" );
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document.write( "Subtract \"20pi\" from all three sides:\r\n" );
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document.write( "\"-38pi\"\"%22%22%3C%22%22\"\"24pi%2Ak\"\"%22%22%3C%22%22\"\"-8pi\"\r\n" );
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document.write( "Divide all three sides by \"24pi\"\r\n" );
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document.write( "\"%28-38pi%29%2F%2824pi%29\"\"%22%22%3C%22%22\"\"%2824pi%2Ak%29%2F%2824pi%29\"\"%22%22%3C%22%22\"\"-8pi%2F%2824pi%29\"\r\n" );
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document.write( "\"%28-19%29%2F%2812%29\"\"%22%22%3C%22%22\"\"k\"\"%22%22%3C%22%22\"\"-1%2F3\"\r\n" );
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document.write( "\"%22-1.583...%22\"\"%22%22%3C%22%22\"\"k\"\"%22%22%3C%22%22\"\"%22-0.333...%22\"\r\n" );
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document.write( "The only integer between those values is k = -1.\r\n" );
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document.write( "So the other solution is \r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"20pi%2F3%2B8pi%2Ak\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"20pi%2F3%2B8pi%28-1%29\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"20pi%2F3-8pi\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"20pi%2F3-24pi%2F3\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"-4pi%2F3\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"-pi%2F3\"\r\n" );
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document.write( "Answer:  \"4pi%2F3\" and \"-4pi%2F3\"\r\n" );
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document.write( "Edwin
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